generatePetersenGraph

Generates a Petersen Graph. The
Petersen Graph is a named graph that consists of 10 vertices and 15 edges, usually drawn as a
five-point star embedded in a pentagon. It is the generalized Petersen graph $GP(5,2)$

Parameters:

targetGraph - receives the generated edges and vertices; if this is non-empty on entry,
the result will be a disconnected graph since generated elements will not be connected
to existing elements

generateDodecahedronGraph

Generates a Dodecahedron
Graph. The skeleton of the dodecahedron (the vertices and edges) form a graph. It is one
of 5 Platonic graphs, each a skeleton of its Platonic solid. It is the generalized Petersen
graph $GP(10,2)$

Parameters:

targetGraph - receives the generated edges and vertices; if this is non-empty on entry,
the result will be a disconnected graph since generated elements will not be connected
to existing elements

generateBuckyBallGraph

Generates a Bucky ball Graph. This
graph is a 3-regular 60-vertex planar graph. Its vertices and edges correspond precisely to
the carbon atoms and bonds in buckminsterfullerene. When embedded on a sphere, its 12
pentagon and 20 hexagon faces are arranged exactly as the sections of a soccer ball.

Parameters:

targetGraph - receives the generated edges and vertices; if this is non-empty on entry,
the result will be a disconnected graph since generated elements will not be connected
to existing elements

generateBidiakisCubeGraph

Generates a Bidiakis cube Graph.
The 12-vertex graph consisting of a cube in which two opposite faces (say, top and bottom)
have edges drawn across them which connect the centers of opposite sides of the faces in such
a way that the orientation of the edges added on top and bottom are perpendicular to each
other.

Parameters:

targetGraph - receives the generated edges and vertices; if this is non-empty on entry,
the result will be a disconnected graph since generated elements will not be connected
to existing elements

generateKittellGraph

Generates the Kittell Graph. The
Kittell graph is a planar graph on 23 nodes and 63 edges that tangles the Kempe chains in
Kempe's algorithm and thus provides an example of how Kempe's supposed proof of the
four-color theorem fails.

Parameters:

targetGraph - receives the generated edges and vertices; if this is non-empty on entry,
the result will be a disconnected graph since generated elements will not be connected
to existing elements